Learn English – I suggest that he go/goes

As @tchrist's Google Ngram shows, it is established idiom, beyond the reach of mere grammatical logic.

And anyway, it's mandative; if it were subjunctive, it should be present subjunctive, It's time something be done.

ADD:
Jespersen, A Modern English Grammar on Historical Principles, Vol 4 (I omit notes indexing citations.):

9.6. After it is (high) time it is usual to use the preterit. Originally this was in the subjunctive because it was looked upon as hypothetical, but as in the majority of instances there was no formal difference between the subjunctive and the indicative, and as the hypothetical element was not so clearly before the mind as in conditional sentences, the indicative came to be used.

English does not have a subjunctive mood, nor a conditional mood.
Despite what you may have been told in school; if you've been misled, I'm sorry about that.

English does have a lot of modal auxiliaries, some of which have meanings (but not grammar)
that reminds scholars of some of the uses of subjunctive and conditional moods in
languages that have them, like Latin or Sanskrit.

But there is no subjunctive, no conditional, and no future tense in English. The constructions that are sometimes given these names are all uses of modal auxiliary verbs, with syntax to match.

This has been explained over and over again, but it's always surprising the first time.

Here are some answers to questions about the so-called "subjunctive" in English.
As you can see, it doesn't work quite the way you have been taught.